Question

Which equation is y=-6x2 + 3x + 2 rewritten in vertex form?

Answer 1

Answer:

The vertex form of the equation is:

$y=-6\,(x-\frac{1}{4})^2+\frac{19}{8}$

Step-by-step explanation:

In order to write the equation in vertex form, we need to find the vertex coordinates. The x-coordinate of the vertex of a parabola of the form:

$y=ax^2+bx+c$

is given by:

$x_{vertex}=\frac{-b}{2\,a}$

which in our case renders:

$x_{vertex}=\frac{-b}{2\,a}\\x_{vertex}=\frac{-3}{-12}\\x_vertex=\frac{1}{4}$

Knowing this, then the y-coordinate of the vertex is obtained by using the x-coordinate of the vertex in the functional form:

$y=-6\,(\frac{1}{4}) ^2+3\,(\frac{1}{4} )+2=\frac{19}{8}$

Then, the equation of the parabola in vertex form becomes:

$y=a\,(x-\frac{1}{4})^2+\frac{19}{8}$

Now we need to find the value of the parameter $"a"$, which since it is the actual leading term of the function in standard form, should be "-6".

Then the vertex form of the equation is:

$y=-6\,(x-\frac{1}{4})^2+\frac{19}{8}$